Surjectivity of the total Clifford invariant and Brauer dimension

Details Surjectivity of the total Clifford invariant and Brauer dimension Surjectivity of the total Clifford invariant and Brauer dimension

2011-08-29

arxiv.org/abs/1108.5728v1

Mathematics

Algebraic Geometry

20 pages, comments welcome

Scientific paper

Merkurjev's theorem---the statement that the 2-torsion of the Brauer group is represented by Clifford algebras of quadratic forms---is in general false when the base is no longer a field. The work of Parimala, Scharlau, and Sridharan proves the existence of smooth complete curves over local fields for which Merkurjev's theorem is equivalent to the existence of a rational theta characteristic. Here we prove that on regular curves over local fields or surfaces over finite fields, replacing the Witt group by the total Witt group of line bundle-valued quadratic forms recovers Merkurjev's theorem: the 2-torsion of the Brauer group is represented by Clifford algebras of line bundle-valued quadratic forms.

Affiliated with

Also associated with

No associations

Rating

Surjectivity of the total Clifford invariant and Brauer dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Surjectivity of the total Clifford invariant and Brauer dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surjectivity of the total Clifford invariant and Brauer dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127404